Question

Cups A and B are cone shaped and have heights of `35 cm` and `23 cm` and openings with radii of `14 cm` and `9 cm`, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

Answer 1

cup `A` will not overflow.

`=28.5` cm

Explanation:

Total volume of cup `B=pir^2h/3=pi(9)^2(23/3)=621pi`
Total volume of cup `A=pir^2h/3=pi(14)^2(35/3)=2286.67pi`
Since volume of cup `B` is less than volume of cup `A`; Contents of cup `B` if poured into cup `A` will not make cup `A` overflow
hence cup `A` will not overflow.

So we have to find `H=?` the height in Cup `A` which will have content of same volume as volume of Cup`B`

`pi(14)^2(H/3)=pi(9)^2(23)`
or

`H/3=(9^2/14^2)(23)=9.5`
or

`H=28.5` cm